Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [statistics]

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.

Statistics is the science of the collection, organization, and interpretation of data. It deals with many aspects of data, which includes the planning of data collection in terms of the design of surveys and experiments. (From Wikipedia)

More specifically, mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and mathematical analysis. (From Wikipedia)

For questions which are more generally about collecting and treating data, it is advised that you post your question on Cross Validated and DSSE.

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What is the difference between standard deviation and variance?

I have been learning discrete probability and know that variance and sd are both measures of spread. I also know that sd is just the variance squared. But I don't know the difference between them. Do they measure different types of spread? Also, I…
user71207
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Difference between a long tail and normal distribution

Wikipedia article about "long tail" says that: A probability distribution is said to have a long tail, if a larger share of population rests within its tail than would under a normal distribution. I am confused about this. Isn't a normal…
radha
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Cramer's V - example and intuition

Hy, I self study statistics and I come across Cramer's V and I search on Google. The result I find didn't explain me so I please to answer this questions. What is measured by Cramer's V? What is an example when Cramer's V is equal to 0 and an…
josf
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Show that $S^2$ is a biased estimator of $\sigma^2$

How did they get from equation (3) to equation (4)? $$S^2 = \frac{1}{n} \sum (X_i - \bar{X})^2 \tag{0}$$ $$E[S^2] = E\Big[\frac{1}{n} \sum (X_i - \bar{X})^2 \Big]\tag{1}$$ $$E[S^2] = E\Bigg[\frac{1}{n} \sum \limits_{i=1}^{n}\Big[~[(X_i -…
Leaky Capacitor
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Given some data, how can I tell how well it fits a (continuous) uniform distribution?

I have a set of $30$ real numbers between zero and one. Let's say that the null hypothesis is that this data set fits a uniform distribution and that the alternative hypothesis is that this data set does not fit a uniform distribution. How would I…
PhiNotPi
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How to estimate CTR (click-through rate)?

How many times banner should be shown to estimate CTR? For example, a banner was shown x times, and was clicked y times. CTR = y/x; How to evaluate incaccuracy of this value?
varan
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Profesor used this property in a statistics class, first that I've seen this

$$ \sum_{i=1}^{n}\left(X_{i}-\mu\right)^{2}=\sum_{i=1}^{n}\left(X_{i}-\bar{X}\right)^{2}+n(\bar{X}-\mu)^{2} $$ My professor didn't prove this, but said it is easy to. I am confused because I can't seem to get it. Would appreciate it if someone could…
Varun Gawande
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Confidence intervals and different methods of sampling

I have two samples collected from the same population, where each sample is collected using a different method of selection, and both samples are large enough for the distribution of the sample distribution of the mean to be normal. Now, when…
JustDanyul
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What makes terms of the sum in variance raise to the power of $2$ not $4$ or $6$?

If I change the power of the variance to $4$ or $6$, do the properties of the new formula remain the same as the old variance formula? If not what is the difference? Variance formula: $$\sigma^2=\frac{\sum(X-\mu)^2}{N}$$
Victor
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Percolation networks in three dimensions by shapes of different sizes

Percolation is something which I feel I understand somewhat intuitively, but it is quite complex as far as I've read, and therefore my expectations may be wrong. It's related to my research in materials science, so I'd like to grasp it better if at…
Nicolau Saker Neto
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Getting P-value While Using Variance

Suppose we observe a random sample of five measurements: 10, 13, 15, 15, 17, from a normal distribution with unknown mean $\mu_1$ and unknown variance $\sigma_1^2$, A second random sample from another normal population with unknown mean $\mu_2$ and…
tuba09
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Cramer-Rao lower bound for exponential distribution

Given a sample $X_1,\dots , X_n$ from a population $X\sim \operatorname {Exp} (\lambda )$, I have to calculate Cramer-Rao bounds for the estimation of $\lambda$ and $\frac 1 \lambda$; I also must determine if there are estimators that limit. Now,…
Dr. Scotti
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Binomial in Statistics

I was asked a question; A student was late for college 0.25 of the time, what is the probability he is late 4 days in one college week. My answer was this: L = Late, N = Not Late L = 0.25, N = 0.75 if its a 7 day week P(L+N)7 = L7 + (7C1)L6 N +…
Mrlemons109
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How to find quartiles using histogram?

Can you suggest how can I find first and third quartiles and median after building histogram from raw data? I can sort the data and find the values, but still how it can be done using the chart...
Bruh
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Covariance basic properties and understanding

Let's consider two random variables $A$ and $B$ having joint probability distribution $P(A,B)$. I would like to understand better the limit cases of the correlation coefficient $r=\frac{C(A,B)}{\sigma(A)\sigma(B)}$ I first show what I understand and…
StarBucK
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